Question: Simplify the following expression: $\dfrac{54t}{18t^3}$ You can assume $t \neq 0$.
Explanation: $ \dfrac{54t}{18t^3} = \dfrac{54}{18} \cdot \dfrac{t}{t^3} $ To simplify $\frac{54}{18}$ , find the greatest common factor (GCD) of $54$ and $18$ $54 = 2 \cdot 3 \cdot 3 \cdot 3$ $18 = 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(54, 18) = 2 \cdot 3 \cdot 3 = 18 $ $ \dfrac{54}{18} \cdot \dfrac{t}{t^3} = \dfrac{18 \cdot 3}{18 \cdot 1} \cdot \dfrac{t}{t^3} $ $\phantom{ \dfrac{54}{18} \cdot \dfrac{1}{3}} = 3 \cdot \dfrac{t}{t^3} $ $ \dfrac{t}{t^3} = \dfrac{t}{t \cdot t \cdot t} = \dfrac{1}{t^2} $ $ 3 \cdot \dfrac{1}{t^2} = \dfrac{3}{t^2} $